mlsanityData to 14 Oct 2026

ProBF: Learning Probabilistic Safety Certificates with Barrier Functions

arXiv 2112.12210 ↗First posted 22 Dec 2021cs.LG cs.SY eess.SYcited by 0

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Abstract (arXiv)

Safety-critical applications require controllers/policies that can guarantee safety with high confidence. The control barrier function is a useful tool to guarantee safety if we have access to the ground-truth system dynamics. In practice, we have inaccurate knowledge of the system dynamics, which can lead to unsafe behaviors due to unmodeled residual dynamics. Learning the residual dynamics with deterministic machine learning models can prevent the unsafe behavior but can fail when the predictions are imperfect. In this situation, a probabilistic learning method that reasons about the uncertainty of its predictions can help provide robust safety margins. In this work, we use a Gaussian process to model the projection of the residual dynamics onto a control barrier function. We propose a novel optimization procedure to generate safe controls that can guarantee safety with high probability. The safety filter is provided with the ability to reason about the uncertainty of the predictions from the GP. We show the efficacy of this method through experiments on Segway and Quadrotor simulations. Our proposed probabilistic approach is able to reduce the number of safety violations significantly as compared to the deterministic approach with a neural network.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 16 of its 30 references that are in the map. First posted on arXiv 22 Dec 2021.

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16 of 30 references.

References · 16

  1. 2016CVXPY: A Python-Embedded Modeling Language for Convex Optimizationcited by 641
  2. 2019Control Barrier Functions: Theory and Applicationscited by 372
  3. 2017Safe Model-based Reinforcement Learning with Stability Guaranteescited by 366
  4. 2019End-to-End Safe Reinforcement Learning through Barrier Functions for Safety-Critical Continuous Control Taskscited by 289
  5. 2016Control Barrier Function Based Quadratic Programs for Safety Critical Systemscited by 287
  6. 2017A General Safety Framework for Learning-Based Control in Uncertain Robotic Systemscited by 163
  7. 2019Learning for Safety-Critical Control with Control Barrier Functionscited by 69
  8. 2020Reinforcement Learning for Safety-Critical Control under Model Uncertainty, using Control Lyapunov Functions and Control Barrier Functionscited by 68
  9. 2017Safe Learning of Quadrotor Dynamics Using Barrier Certificatescited by 35
  10. 2020Safe Multi-Agent Interaction through Robust Control Barrier Functions with Learned Uncertaintiescited by 20
  11. 2019Episodic Learning with Control Lyapunov Functions for Uncertain Robotic Systemscited by 19
  12. 2019Multi-Robot Collision Avoidance under Uncertainty with Probabilistic Safety Barrier Certificatescited by 13
4 more
  1. 2021Pointwise Feasibility of Gaussian Process-based Safety-Critical Control under Model Uncertaintycited by 13
  2. 2020Gaussian Process-based Min-norm Stabilizing Controller for Control-Affine Systems with Uncertain Input Effects and Dynamicscited by 12
  3. 2019Probabilistic Safety Constraints for Learned High Relative Degree System Dynamicscited by 9
  4. 2020Learning Control Barrier Functions with High Relative Degree for Safety-Critical Controlcited by 6

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